Permutations

Permutation

OBJECTIVES

• Analyze each word problem to identify the needed data

• Solve problems involving linear permutation, circular permutations and distinguishable permutation

• Participate actively during the discussion

REVIEW

Read each question carefully and click on the button next to your response that is based on information covered on our previous lesson.

Multiple Select

1. It refers to the possible arrangement of an object.

• Permutation

• Combination

Multiple Select

2. What is the formula in finding Linear Permutation taken at all time?

• $$P\left(n,n\right)=n!$$  

• $$P\left(n,r\right)=\frac{n!}{\left(n-r\right)!}$$  

Multiple Select

3 . What is the formula in finding Linear Permutation taken at r time?

• $$P\left(n,n\right)=n!$$  

• $$P\left(n,r\right)=\frac{n!}{\left(n-r\right)!}$$  

Multiple Select

4 . What is the formula in finding Circular  Permutation 

• $$P\left(n,n\right)=n!$$  

• $$P=\left(n-1\right)!$$  

Multiple Select

5 . What is the formula in finding Distinguishable Permutation 

• $$P\left(n,r\right)=\frac{n!}{\left(n-r\right)!}$$  

• $$P=\frac{n!}{p!q!r!..}$$  

Click on the button next to your response.

Multiple Select

$$1.\ \ \ What\ is\ P\left(3,3\right)?$$  

• 6

• 12

Multiple Select

$$2.\ \ \ What\ is\ P\left(8,5\right)?$$  

• 326

• 336

Multiple Select

$$3.\ \ \ Evaluate\ \ P\left(\frac{8!}{3!}\right)?$$  

• 6,720

• 6,520

Multiple Select

$$4.\ \ \ Evaluate\ \ \ P\left(\frac{9!}{4!2!}\right)?$$  

• 30,240

• 30,250

Multiple Select

$$Evaluate\ \ P=\left(n-1\right)!\ where\ \ n=4$$  

• 12

• 6

Open Ended

Are there any clarification, questions regarding to our lesson?

SOLVING PROBLEMS INVOLVING PERMUTATION

Permutation of an object taken all at the time

Example No.1 

• A teacher wants to assign 4 different tasks to her 4 students. in how many ways can she do it?

•  $P\left(n,r\right)=n!\ \ \ \ \ \ \ \ where\ n=4\ ;\ r=4$ 

•  $P\left(4,4\right)=4!$  

•  24 ways

Example No.2

• In how many  different ways can 12 people occupy 12 seats in front row of a mini theather?

•  $P\left(n,r\right)=n!\ \ \ \ \ \ \ \ where\ n=12\ ;\ r=12$ 

•  $P\left(12,12\right)=12!$  

•  479,001,600 ways

Open Ended

Are there any clarification, questions regarding to our lesson?

Permutation of an object taken r at the time

Example No.3 

• In how many  different ways can 5 bicycles  be parked if there are 7 available parking spaces?

•  $P\left(n,r\right)=\frac{n!}{\left(n-r\right)!}\ \ \ \ \ \ \ where\ n=7\ ;\ r=5$ 

•  $P\left(7,5\right)=\frac{7!}{\left(7-5\right)!}$  

•   $P=\frac{7!}{2!}$  

• 2,520 different ways

Example No.4 

• If there are 10 people and only 6 chairs are available, in how many ways they can be seated?

•  $P\left(n,r\right)=\frac{n!}{\left(n-r\right)!}\ \ \ \ \ \ \ where\ n=10\ ;\ r=6$ 

•  $P\left(7,5\right)=\frac{10!}{\left(10-6\right)!}$  

•   $P=\frac{10!}{4!}$  

• 151,200 different ways

Open Ended

Are there any clarification, questions regarding to our lesson?

Circular Permutation

Example No.5

• Find the number of different ways that the family of 6 can be seated around the circular table with 6 chairs?

•  $P=\left(n-1\right)!\ \ \ \ \ \ \ where\ n=6\$ 

•  $P=\left(6-1\right)!$  

•   $P=5!$  

• 120 different ways

Example No.6

• There are 12 people in a dinner gathering. In how many ways can the host arrange his guests around the table

•  $P=\left(n-1\right)!\ \ \ \ \ \ \ where\ n=12$ 

•  $P=\left(12-1\right)!$  

•   $P=11!$  

• 39,916,800 different ways

Open Ended

Are there any clarification, questions regarding to our lesson?

Distinguishable Permutation

• Let us use Filipino traits in solving permutation

• 
  

Example No.7

• In how many different ways can the letters  of MAKADIYOS be arranged?

•  $P=\frac{n!}{\left(p!\right)}!\ \ \ \ \ \ \ where\ n=9\ ;\ q=2$ 

•  $P=\frac{9!}{2!}$  

• 181,440 different ways

Example No.8

• In how many different ways can the letters  of MAPAGPAKUMBABA be arranged?

•  $P=\frac{n!}{\left(p!q!r!s!\right)}\ \ \ where\ n=14\ ;\$  $\ p\ \left(M\right)=2\ \ ;q\ \left(A\right)\ =5\ ;\ r\ \left(P\right)=2\ ;\ s\ \left(B\right)=2$ 

•  $P=\frac{14!}{\left(2!5!2!2!\right)}$  

• 90,810,720 different ways

Open Ended

Are there any clarification, questions regarding to our lesson?

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 There are 8 basketball teams competing for the top 4 standings in order to move up to the semi finals. Find the number of possible rankings of the four top teams?

 In how many ways can 5 people occupy 5 seats in front of a mini- theater?

Find the number of different ways that a family of 7 can be seated in a round table with 7 chairs?

 How many distinguishable permutations are there for the letters of the word COMMITTEE?

Open Ended

Are there any clarification, questions regarding to our lesson?

Evaluation

Identify what is being asked in each question.

Multiple Choice

1. Find the number of permutation of the letters of the word MOMMY.?

• a. 8

• b. 12

• c. 20

• d. 24

Multiple Choice

2. A stockbroker wants to assign 12 new clients equally to 4 of its sales agents. In how many different way can this be done?

• a. 369,600

• b. 369,800

• c. 369,900

• d. 379,600

Multiple Choice

3. Bobby applied for landline phone in his new house. He was given the number 7-630-8380. How many distinguishable permutations are there in his telephone number?

• a. 5,00

• b. 5,040

• c. 5,060

• d. 5,080

Multiple Choice

4. How many ways can you arrange books of the same kind if there are 4 Math books , 3 Science books and 2 English books in shelf?

• a. 1,260

• b. 1,264

• c. 1,270

• d. 1,274

Multiple Choice

5. Find the number of permutation if five 1,000 peso bills, three 100-peso bills and two 50 peso bills be arranged in a wallet.

• a. 2,500

• b. 2,510

• c. 2,515

• d. 2,520

Thank You!